A unified fluid-structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-α scheme are used for the spatial and temporal discretization. The membrane discretization is based on curvilinear surface elements that can describe large deformations and rotations, and also provide a straightforward description for contact. The fluid is described by the incompressible Navier-Stokes equations, and its discretization is based on stabilized Petrov-Galerkin FE. The coupling between fluid and structure uses a conforming sharp interface discretization, and the resulting non-linear FE equations are solved monolithically within the Newton-Raphson scheme. An arbitrary Lagrangian-Eulerian formulation is used for the fluid in order to account for the mesh motion around the structure. The formulation is very general and admits diverse applications that include contact at free surfaces. This is demonstrated by two analytical and three numerical examples exhibiting strong coupling between fluid and structure. The examples include balloon inflation, droplet rolling and flapping flags. They span a Reynolds-number range from 0.001 to 2000. One of the examples considers the extension to rotation-free shells using isogeometric FE.
Swirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners, turbines and jet engines. To simulate the highly nonlinear dynamics of the flow, it is necessary to use high-order numerical methods, leading to increased computational cost. To be able to perform simulations in acceptable turn-around time, an available LES code for solving the filtered compressible Navier-Stokes equations in cylindrical coordinates using compact finite-difference schemes was parallelized for massively-parallel architectures. The parallelization was done following the ghost-cell approach for filtering in the three spatial directions. The inter-process communication is handled using the message passing interface (MPI). The weak and strong scaling properties of the code indicate that it can be used for massively parallel simulations using several thousand processors.
Circular jet flows play an important role for many technical applications. Realistic simulations of such flows require modelling of the nozzle geometry to represent the turbulent state of the boundary layer at the nozzle exit. An available high-order finitedifference code for solving the compressible Navier-Stokes equations on a cylindrical grid was adapted to account for the nozzle geometry within the simulation domain. The code was parallelized using the message-passing interface MPI to be able to complete the simulations within acceptable turn-around times. Validation of the implementation was performed by checking the convergence behaviour of the spatial discretization schemes.
We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier-Stokes equations in cylindrical coordinates using high-order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point-flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up-and downstream.
Simulation methodologySwirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners, turbines and jet engines. At the stage of vortex breakdown the flow is dominated by a conical shear layer and a large recirculation zone around the jet axis. In our group we developed a numerical tool to investigate swirling jet flow undergoing vortex breakdown (see [1] and references therein). For spatial derivatives we use high-order finite difference schemes [2] and a spectral method. The time integration scheme is a LDDRK method of fourth order [3]. We included a canonical nozzle with isothermal wall into our computational setup to account for more realistic inflow boundary conditions [4]. This modification is mainly motivated by the observation of [5] that the breakdown of the swirling jet interacts with the inflow boundary treatment leading to the possible prevention of naturally developing helical modes. We simulate a swirling jet at Re = R · u zc /ν c = 5000 At the inflow Dirichlet boundary conditions are applied to all five conservative variables supplemented with a sponge layer to prevent reflections of upstream travelling waves. A turbulent pipe flow profile is used for the axial velocity component, u z = 1 − r 7 and the radial velocity, u r , is identically zero. The fluid is in solid body rotation, u θ = S · r, within the nozzle and irrotational outside, where S = u θmax /u zmax = 1.0 is the swirl number. The pressure distribution is derived from the radial component of the Navier-Stokes equations in cylindrical coordinates and integrated numerically. The density is calculated from the equation of state thereafter. At the outflow and in the far-field non-reflecting boundary conditions are implemented [6]. Additionally a sponge layer is used in the far-field acting on the density ρ and pressure p to prevent a mean pressure drift. At the nozzle wall, which is of length 2.5R, all velocities u i and the temperature T are set according to the inflow profiles. The whole flow field is initialized according to the inflow profiles and random noise of small amplitude 10 −5 is added. Figure 1a shows an instantaneous snapshot of...
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